All Questions

Permanent of biadjacency of bipartite graphs is the number of perfect matchings. In the case of planar graphs we can obtain an orientation with sign changes and get away with computing the determinant ...

Given a $\pm1$ matrix $M$ of rank $r$ let the largest subdeterminant be $d$ and let the largest subpermanent be $p$. Are there relations/bounds that connect $r$, $d$ and $p$? Are there geometric and ...

Planar graph permanent can be reduced to determinants and so statistics should be amenable. Pick a uniformly random bipartite planar graph $G$ with $n$ vertices of each color and choose new additional ...

What is the closed form of this permanent? (similar to the Cauchy determinant) \begin{aligned} f(z_1,z_2,\cdots,z_N,w_1,w_2,\cdots,w_N)=\left[ \small{\begin{matrix} \frac{1}{(z_1-w_1)^2} && \...

Motivated by my study of determinants and permanents, here I present several conjectures on $p$-adic congruences involving permutations. As usual, we let $S_n$ be the symmetric group consisting of all ...

The slides here provide a way to get a pfaffian orientation from Minimum Spanning Tree. MST can be found in linear time if graph is planar and weights are $1$ and the slides give a linear time ...